Nonuniqueness in the close-coupling method for e-He scattering

We present a general analysis of the close-coupling equations for e-He scattering. We show why the standard close-coupling expansion gives rise to nonunique solutions and, by characterizing the manifold of nonunique solutions, are able to construct equations with a unique solution. Our analysis concentrates on two models of target states; a frozen-core model in which one of the electrons is restricted to the 1s He+ orbital, as has been used with great success recently, and also a model which uses full configuration-interaction target states. We develop modified close-coupling equations by projecting out spurious solutions. A subtle difference between frozen-core and configuration-interaction models with respect to the manner in which antisymmetrization is incorporated is noted. A calculation to illustrate the theory is presented.